Additive nonparametric regression estimation via backfitting and marginal integration: Small sample performance

Abstract

In this paper, we conducted a Monte Carlo investigation to reveal some characteristics of finite sample distributions of the Backfitting (B) and Marginal Integration (MI) estimators for an additive bivariate regression. We are particularly interested in providing some evidence on how the different methods for the selection of bandwidth, such as the plug-in method, influence the finite sample properties of the MI and B estimators. We are also interested in providing evidence on the behavior of different bandwidth estimators relatively to the optimal sequence that minimizes a chosen loss function. The impact of ignoring the dependency between regressors is also investigated. Finally, differently from what occurs at the present time, when the B and MI estimators are used ad-hoc, our objective is to provide information that allows for a more accurate comparison of these two competing alternatives in a finite sample setting.